Hello OP, just wanted to say that a relationship should not cause so much angst over something so small. If he is struggling to cope with this, how will he cope in day to day life with problems more complex. If you live together, will he just ignore you for days on end? Your health is suffering from this anxiety and you cannot be your best self when you're constantly on edge about what may trigger him. You also have children and need stability, reliability and consistency in your life (and theirs), and he doesn't seem to offer it.
He may be the loveliest guy but that doesn't mean he is good at relationships, or certainly a relationship with you. My partner is mildly on the spectrum too, and his natural instinct is to shut down and retreat. However, the first time he tried to do it (after a massive row tbf), I very clearly explained I would not tolerate stonewalling. Since then he will let me know he needs some hours to process (hours, not days mind), doesn't go off grid i.e if i need him I know he will reply. I, let him have his space, and when he comes back, discuss it calmly with him. That is a timeout that works for both of us. However, this is only when we have proper rows that are very infrequent. If he had gone no contact over something so minor, I would have walked away. As life is too short to be living in such anxiety.
Please don't let his needs override yours. If he cares about you, he should feel bad for causing you this much anxiety with just not knowing.. and want to find a way to compromise so you both can feel at ease. If he does come back, you should ensure he gets that it is unacceptable to just vanish with no contact in a relationship. And if he doesn't or can't understand that, I don't think you'll ever sleep completely peacefully being with him. You'll always wonder when he'll next vanish or ghost or just break up with you.